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libgeometry: add quaternion sandwich product functions
also took the chance to remove the semicolons from the function signatures in the manpage synopsis, as is custom in the other manuals.
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rodri
parent
84170d89b7
commit
65ea63e521
3 changed files with 115 additions and 82 deletions
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@ -122,6 +122,8 @@ Quaternion invq(Quaternion);
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double qlen(Quaternion);
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Quaternion normq(Quaternion);
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Quaternion slerp(Quaternion, Quaternion, double);
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Quaternion qsandwich(Quaternion, Quaternion);
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Point3 qsandwichpt3(Quaternion, Point3);
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Point3 qrotate(Point3, Point3, double);
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/* RFrame */
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@ -56,107 +56,109 @@ struct Triangle3 {
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};
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.PB
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/* utils */
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double flerp(double a, double b, double t);
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double fberp(double a, double b, double c, Point3 bc);
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double fclamp(double n, double min, double max);
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double flerp(double a, double b, double t)
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double fberp(double a, double b, double c, Point3 bc)
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double fclamp(double n, double min, double max)
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.PB
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/* Point2 */
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Point2 Pt2(double x, double y, double w);
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Point2 Vec2(double x, double y);
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Point2 addpt2(Point2 a, Point2 b);
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Point2 subpt2(Point2 a, Point2 b);
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Point2 mulpt2(Point2 p, double s);
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Point2 divpt2(Point2 p, double s);
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Point2 lerp2(Point2 a, Point2 b, double t);
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Point2 berp2(Point2 a, Point2 b, Point2 c, Point3 bc);
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double dotvec2(Point2 a, Point2 b);
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double vec2len(Point2 v);
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Point2 normvec2(Point2 v);
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int edgeptcmp(Point2 e0, Point2 e1, Point2 p);
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Point2 Pt2(double x, double y, double w)
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Point2 Vec2(double x, double y)
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Point2 addpt2(Point2 a, Point2 b)
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Point2 subpt2(Point2 a, Point2 b)
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Point2 mulpt2(Point2 p, double s)
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Point2 divpt2(Point2 p, double s)
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Point2 lerp2(Point2 a, Point2 b, double t)
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Point2 berp2(Point2 a, Point2 b, Point2 c, Point3 bc)
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double dotvec2(Point2 a, Point2 b)
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double vec2len(Point2 v)
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Point2 normvec2(Point2 v)
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int edgeptcmp(Point2 e0, Point2 e1, Point2 p)
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int ptinpoly(Point2 p, Point2 *pts, ulong npts)
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.PB
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/* Point3 */
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Point3 Pt3(double x, double y, double z, double w);
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Point3 Vec3(double x, double y, double z);
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Point3 addpt3(Point3 a, Point3 b);
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Point3 subpt3(Point3 a, Point3 b);
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Point3 mulpt3(Point3 p, double s);
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Point3 divpt3(Point3 p, double s);
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Point3 lerp3(Point3 a, Point3 b, double t);
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Point3 berp3(Point3 a, Point3 b, Point3 c, Point3 bc);
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double dotvec3(Point3 a, Point3 b);
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Point3 crossvec3(Point3 a, Point3 b);
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double vec3len(Point3 v);
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Point3 normvec3(Point3 v);
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Point3 Pt3(double x, double y, double z, double w)
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Point3 Vec3(double x, double y, double z)
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Point3 addpt3(Point3 a, Point3 b)
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Point3 subpt3(Point3 a, Point3 b)
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Point3 mulpt3(Point3 p, double s)
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Point3 divpt3(Point3 p, double s)
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Point3 lerp3(Point3 a, Point3 b, double t)
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Point3 berp3(Point3 a, Point3 b, Point3 c, Point3 bc)
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double dotvec3(Point3 a, Point3 b)
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Point3 crossvec3(Point3 a, Point3 b)
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double vec3len(Point3 v)
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Point3 normvec3(Point3 v)
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int lineXsphere(Point3 *rp, Point3 p0, Point3 p1,
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Point3 c, double rad, int isaray);
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Point3 c, double rad, int isaray)
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.PB
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/* Matrix */
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void identity(Matrix m);
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void addm(Matrix a, Matrix b);
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void subm(Matrix a, Matrix b);
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void mulm(Matrix a, Matrix b);
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void smulm(Matrix m, double s);
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void transposem(Matrix m);
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double detm(Matrix m);
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double tracem(Matrix m);
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double minorm(Matrix m, int row, int col);
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double cofactorm(Matrix m, int row, int col);
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void adjm(Matrix m);
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void invm(Matrix m);
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Point2 xform(Point2 p, Matrix m);
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void identity(Matrix m)
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void addm(Matrix a, Matrix b)
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void subm(Matrix a, Matrix b)
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void mulm(Matrix a, Matrix b)
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void smulm(Matrix m, double s)
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void transposem(Matrix m)
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double detm(Matrix m)
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double tracem(Matrix m)
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double minorm(Matrix m, int row, int col)
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double cofactorm(Matrix m, int row, int col)
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void adjm(Matrix m)
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void invm(Matrix m)
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Point2 xform(Point2 p, Matrix m)
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.PB
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/* Matrix3 */
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void identity3(Matrix3 m);
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void addm3(Matrix3 a, Matrix3 b);
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void subm3(Matrix3 a, Matrix3 b);
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void mulm3(Matrix3 a, Matrix3 b);
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void smulm3(Matrix3 m, double s);
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void transposem3(Matrix3 m);
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double detm3(Matrix3 m);
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double tracem3(Matrix3 m);
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double minorm3(Matrix3 m, int row, int col);
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double cofactorm3(Matrix3 m, int row, int col);
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void adjm3(Matrix3 m);
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void invm3(Matrix3 m);
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Point3 xform3(Point3 p, Matrix3 m);
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void identity3(Matrix3 m)
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void addm3(Matrix3 a, Matrix3 b)
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void subm3(Matrix3 a, Matrix3 b)
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void mulm3(Matrix3 a, Matrix3 b)
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void smulm3(Matrix3 m, double s)
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void transposem3(Matrix3 m)
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double detm3(Matrix3 m)
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double tracem3(Matrix3 m)
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double minorm3(Matrix3 m, int row, int col)
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double cofactorm3(Matrix3 m, int row, int col)
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void adjm3(Matrix3 m)
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void invm3(Matrix3 m)
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Point3 xform3(Point3 p, Matrix3 m)
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.PB
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/* Quaternion */
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Quaternion Quat(double r, double i, double j, double k);
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Quaternion Quatvec(double r, Point3 v);
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Quaternion addq(Quaternion a, Quaternion b);
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Quaternion subq(Quaternion a, Quaternion b);
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Quaternion mulq(Quaternion q, Quaternion r);
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Quaternion smulq(Quaternion q, double s);
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Quaternion sdivq(Quaternion q, double s);
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double dotq(Quaternion q, Quaternion r);
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Quaternion invq(Quaternion q);
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double qlen(Quaternion q);
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Quaternion normq(Quaternion q);
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Quaternion slerp(Quaternion q, Quaternion r, double t);
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Point3 qrotate(Point3 p, Point3 axis, double θ);
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Quaternion Quat(double r, double i, double j, double k)
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Quaternion Quatvec(double r, Point3 v)
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Quaternion addq(Quaternion a, Quaternion b)
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Quaternion subq(Quaternion a, Quaternion b)
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Quaternion mulq(Quaternion q, Quaternion r)
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Quaternion smulq(Quaternion q, double s)
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Quaternion sdivq(Quaternion q, double s)
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double dotq(Quaternion q, Quaternion r)
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Quaternion invq(Quaternion q)
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double qlen(Quaternion q)
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Quaternion normq(Quaternion q)
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Quaternion slerp(Quaternion q, Quaternion r, double t)
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Quaternion qsandwich(Quaternion q, Quaternion r)
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Point3 qsandwichpt3(Quaternion q, Point3 p)
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Point3 qrotate(Point3 p, Point3 axis, double θ)
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.PB
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/* RFrame */
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void rframematrix(Matrix, RFrame);
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void rframematrix3(Matrix3, RFrame3);
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Point2 rframexform(Point2 p, RFrame rf);
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Point3 rframexform3(Point3 p, RFrame3 rf);
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Point2 invrframexform(Point2 p, RFrame rf);
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Point3 invrframexform3(Point3 p, RFrame3 rf);
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void rframematrix(Matrix, RFrame)
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void rframematrix3(Matrix3, RFrame3)
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Point2 rframexform(Point2 p, RFrame rf)
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Point3 rframexform3(Point3 p, RFrame3 rf)
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Point2 invrframexform(Point2 p, RFrame rf)
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Point3 invrframexform3(Point3 p, RFrame3 rf)
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.PB
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/* Triangle2 */
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Point2 centroid(Triangle2 t);
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Point3 barycoords(Triangle2 t, Point2 p);
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Point2 centroid(Triangle2 t)
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Point3 barycoords(Triangle2 t, Point2 p)
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.PB
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/* Triangle3 */
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Point3 centroid3(Triangle3 t);
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Point3 centroid3(Triangle3 t)
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.PB
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/* Fmt */
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#pragma varargck type "v" Point2
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#pragma varargck type "V" Point3
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int vfmt(Fmt*);
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int Vfmt(Fmt*);
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void GEOMfmtinstall(void);
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int vfmt(Fmt*)
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int Vfmt(Fmt*)
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void GEOMfmtinstall(void)
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.SH DESCRIPTION
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This library provides routines to operate with homogeneous coordinates
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in 2D and 3D projective spaces by means of points, matrices,
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@ -629,6 +631,21 @@ by a factor of
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.IR t ,
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and returns the result.
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.TP
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.B qsandwich(\fIq\fP,\fIr\fP)
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Returns the result of "sandwiching"
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.I q
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with
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.IR r ,
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i.e. r' = qrq⁻¹.
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.TP
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.B qsandwichpt3(\fIq\fP,\fIp\fP)
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Same as
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.IR qsandwich (2),
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but treating
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.I p
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as a pure quaternion when computing the product, and keeping its
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projective coordinate (w) intact.
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.TP
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.B qrotate(\fIp\fP,\fIaxis\fP,\fIθ\fP)
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Returns the result of rotating the point
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.I p
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@ -96,13 +96,27 @@ slerp(Quaternion q, Quaternion r, double t)
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return addq(smulq(q, cos(θ)), smulq(v, sin(θ))); /* q cos(θ) + v sin(θ) */
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}
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Quaternion
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qsandwich(Quaternion q, Quaternion p)
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{
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return mulq(mulq(q, p), invq(q)); /* qpq⁻¹ */
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}
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Point3
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qsandwichpt3(Quaternion q, Point3 p)
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{
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Quaternion r;
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r = qsandwich(q, Quatvec(0, p));
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return Pt3(r.i, r.j, r.k, p.w);
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}
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Point3
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qrotate(Point3 p, Point3 axis, double θ)
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{
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Quaternion qaxis, qr;
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Quaternion qaxis;
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θ /= 2;
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qaxis = Quatvec(cos(θ), mulpt3(axis, sin(θ)));
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qr = mulq(mulq(qaxis, Quatvec(0, p)), invq(qaxis)); /* qpq⁻¹ */
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return Pt3(qr.i, qr.j, qr.k, p.w);
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return qsandwichpt3(qaxis, p);
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}
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